The final examination papers and answers of the eighth grade of Beijing Normal University are urgent, and the exam will be taken the day after tomorrow.

1. Fill in the blanks (65438+ 0 points per grid, ***20 points):

The square roots of 1 and 5 are _ _ _ _ _, the arithmetic square root of 32 is _ _ _ _ _, and the cube root of -8 is _ _ _ _ _.

2. Simplification: (1) (2), (3) = _ _ _.

3. As shown in Figure 1, Figure ① passes through.

After _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

The shape ② changes from _ _ _ _ _ to Figure ③,

Graph ③ changes into graph ④ through _ _ _ _ _ _ _.

4. You can spell out _ _ _ _ _ _ _ kinds of parallelograms with two identical triangular rulers (the one with an angle of 30).

5. Estimation: (1) _ (error is less than1)

6. It is known that in quadrilateral ABCD, AB = CD. To make the quadrilateral ABCD a parallelogram, you need to add _ _ _ _ _ _ _. Just fill in one condition that you think is correct.

7. If the sum of the inner angles of a polygon is 1800, which is more than three times the sum of the outer angles, then its

The number of edges is _ _ _ _ _ _.

8. The unit price of a certain rice is 2.4 yuan/kg, and the cost of buying X kg of rice is Y yuan, so the functional relationship between X and Y is

9 .. as shown in the figure, linear l linear function y=kx+b,

Then b=, k=

10 .. if, then x =；; y= .

1 1 ... A workshop processes parts in one day as follows: 2 people process 18 parts, 1 personal processing 14 parts, and 4 people process 1 1 parts./klc

2. Multiple choice questions (2 points for each question, 20 points for * * *):

12. Figure 4 is a rectangular concrete playground in our school. If a student wants to

From angle a to angle c, at least ()

140

13, of the following statements, the correct one is ()

① Infinite decimals are irrational numbers; ② Irrational numbers are all unreasonably restricted decimals;

③ Numbers with radical signs are irrational numbers; ④-2 is the square root of 4.

A.①③ B. ①②③ C. ③④ D. ②④

14. As shown in Figure 5, it is known that point O is the intersection of three heights of regular triangle ABC.

Now ⊿AOB must rotate at least a few degrees around point O, and then coincide with ⊿BOC. ()

A.60 B. 120 C. 240 D. 360

15, and the number one-to-one corresponding to the points on the number axis is ()

A. natural number B. rational number C. irrational number D. real number

16, as shown in Figure 6. In ABCD, E and F are the midpoint of AB and CD respectively, and DE, EF and BF are connected, then the parallelogram in Figure * * * has ().

A.2 B.4 C.6 D.8

17. The distance of point m (-3,4) from the origin is () unit length.

A.3 B. 4 C. 5 D. 7。

18. 10 The average value of data is 12, and the average value of 20 data is 15, so the average value of all 30 data is ().

12 15 c 13.5d 14

Three. Simplification (3 points for each small question, 20 points for * * *):

19.20.

2 1. Used as a method for solving equations of images;

Four, answer questions (5 points for each question, ***30 points)

After translation, the AB side of the triangle moves to EF, and the translated triangle is finished. How many ways can you give?

23. As shown in the figure, in □ABCD, AC and BD intersect at point O, AB ⊥ AC, ∠ DAC = 45 AC = 2, and find the length of BD.

Christian era

B.C.

24. It is known that in a square ABCD, points E and F are the midpoint of AD and BC, respectively.

( 1)△ABE?△CDF？ (2) Is the quadrilateral BFDE a parallelogram?

The second century ad

B F C

25. the point P 1 is the symmetrical point of p (-3,5) about the x axis, and the first function passes through P 1 and a (1, 2).

Find the expression of this linear function and draw the image of this linear function.

26. Our school implements small class teaching in the eighth grade. If there are 20 students in each classroom, there are three classrooms missing. If there are 24 students in each classroom, then one classroom will be vacant. How many classrooms are there in this school? How many people are there in the eighth grade?

27. Liang Xiao's family recently bought a house. Prepare the bedroom with wooden floor when decorating. Tile the living room. According to the market survey, the wages for flooring with these two materials are different. According to the floor area, Xiao Liang has separately budgeted the living room and the living room paving costs (the cost of purchasing materials and wages). Through the list, x(m2) is used to represent the floor area, and Y (yuan) is used to represent the floor cost. As the picture shows, please answer the following questions according to the information provided in the picture.

(1) What is the budget for laying rooms? _ _ _ _ _ Yuan/m2? , the living room laying cost _ _ _ yuan /m? ;

(2) Table setting bedroom laying cost Y yuan, area x(m? ) is _ _ _ _. Represents cost y (yuan) and area x(m? ) is _ _ _ _ _ _ _.

(3) Known in Xiao Jing's budget. Laying 1m? Tiles are more expensive than wooden floors in 5 yuan; Buy 1m? Did you buy the tiles at 1m? 3/4 of the cost of wood flooring. So, how much does it cost per square meter to lay wooden floors and tiles? How much does it cost per square meter to buy wooden floors and tiles?

room

living room

answer

a 1)； 3; -2

2) ( 1)3 (2)5 (3)

3) Axisymmetric translational rotation

4) Three kinds

5)4 or 5

6)AB‖CD or AD=BC, etc.

7)9 sides

8)y=2.4x(x≥0)

9)3; -

10) 1; - 1

1 1) 14. 1; 14; 14

two

12)C； 13) 14)B 15)D

16) 17)C 18)D

three

19) 1- 20)

2 1)

22)3 kinds

23)2

24) Omission

25)y= x-

26)2 1 room; 480 people

27) 135; 1 10;

y = 135 x； y= 1 10x

Labor cost of floor: 15 yuan/㎡; Handmade tiles: 20 yuan/㎡.

Floor material cost: 120 yuan/㎡; Ceramic tile material cost: 90 yuan/㎡.

Eight grades last semester math final review questions.

First, fill it out carefully.

Football lottery winners 0502 1 lottery results

Lucky draw date: May 23rd, 2005. Deadline for exchange: June 20, 2005.

Atalanta Cagliari Chievo Lazio Livorno Bresi Palma Sampdoria Stuga Nuremberg Kayes Birfidotfreiburg.

0 1 3 1 1 3 1 0 0 0 0 0 3 0

1. Observe the results of Chinese football lottery.

Lottery announcement 0502 1, reply

Answer the question: This lottery is over.

"1" in fruits (used for numbers)

The current frequency is "0"

The frequency of occurrence is.

2. Class 5, Grade 8, a school 60

In an English test, 45% students got excellent grades. In the fan-shaped statistical chart, the fan-shaped central angle of these students is degrees; A good fan-shaped central angle is 120, so there are good students.

3. Zhang Sao, a female migrant worker, is re-employed to do a small business of fast food box lunch. The sales in the first five days are as follows: 50 boxes on the first day, 62 boxes on the second day, 57 boxes on the first day, 70 boxes on the first day and 78 boxes on the first day. In order to clearly reflect the sales situation of box lunch in the first five days, we must choose to make a statistical chart.

Xiao Zhang and Xiao Li went to practice shooting. After the first round of 10, their results are as shown in the figure. Usually the scores of novices are not stable, so according to the information in the picture, it is estimated that novices are between Xiao Zhang and Xiao Li.

The picture below shows a histogram of rainfall in a rainy season drawn by Xiao Ming.

(1) The total rainfall this week is about mm;

(2) If the daily rainfall is above 25mm, which days will it rain heavily this week? .

6. There are 100 students taking two scientific and technological knowledge tests. This bar chart shows the score distribution of the two tests. Please answer the following questions according to the information provided by the bar chart (fill in the answers on the horizontal lines in the questions);

(1) The lowest score of the two exams is in the initial test; (2) The initial test is relatively easy;

7. After sorting, a set of data is divided into four groups. The frequencies of the first, second and third groups are 0. 1, 0.3 and 0.4 respectively. The frequency of the first group is 5, so the frequency of the fourth group is * * *.

8. After grouping a sample data with a capacity of 20, the group spacing and frequency are as follows:10 < ≤ 20,2; 20< ≤30,3; 30< ≤40,4; 40< ≤50,5; 50< ≤60,4; 60 < ≤ 70,2. Then the frequency of the sample at 10 < ≤ 50 is ().

A.0.20 B. 0.25 C. 0.50 D. 0.70

Second, choose a choice carefully.

1. The following numbers can be used to indicate the frequency () (a)-0.1(b)1.2 (c) 0.4 (d).

2. The sector accounts for 30% of the circle in the sector statistical chart, so the central angle of the sector at this time is ()

65 438+020 65 438+008 90 60

3. Divide 100 data into 8 parts.

Group, as shown in the following table: then the sixth group's

The frequency is ()

12(B) 13(C) 14(D) 15

4. Girls in A school account for 50% of the total number of students in the school, and boys in B school account for 50% of the total number of students in the school. Compare the number of girls in these two schools ()

There are more schools in A than in B. There are as many schools in B as in A.

5. The figure below shows the statistics of water consumption and population in a certain area. In the year when the average daily water consumption was 4 million tons, the population was about ().

(a) 6.5438+800,000 (b) 2 million (c) 3 million (d) 4 million.

6. A set of data 63, 65, 67,

The frequency of data between 69, 66, 64, 66, 64, 65, 68, 64.5 and 66.5 is () (A)0.4 (B)0.5 (C)5 (D)4.

7. In the first quarter of 2005, the rapid development of ten major industries such as steel and new materials, automobile and other machinery manufacturing, tobacco and food, photoelectric information, petrochemical industry and environmental protection promoted the rapid growth of Wuhan's national economy. Among them, the production scale of the top six industries in the first quarter accounted for 27%, 18% and 18% of the total production scale of the top ten industries in the same period respectively.

It is known that the scale of environmental protection production in the first quarter is about 2.7 billion yuan, so the total production scale of the top ten industries in the first quarter and the number of industries with the statistical scale exceeding 4 billion yuan are () respectively.

(a) about 43.2 billion yuan, 3 (B) about 43.2 billion yuan, 4

8. The picture shows the fan-shaped distribution of Xiao Gang's daily schedule.

Statistics. If Xiao Gang wants to spend his reading time every day,

When it is adjusted to 2, then his reading time needs to be increased ()

(1) 15. (B)48。 60 years old. (D) 105。

Third, answer seriously.

1. Figures ① and ② are two bar charts drawn by Li Xiao according to the number of boys and girls in three grades in his school.

(1) Which of the two pictures can better reflect the total number of students in all grades of the school? Which graph can compare with

Comparison of the number of boys and girls in each grade?

(2) Please draw the fan-shaped statistical chart in Figure ③ according to the number of students of all grades in our school.

2. China Football League A ended the first half of the match on June 1 1. Ranked as follows. Please answer the following questions according to the information provided in the table:

(1) Complete the bar chart in the chart;

(2) Which team conceded at least 14 goals in the league? Which team lost the most games?

(3) What percentage of teams scored more than 20 goals (accurate to 1%)?

Rank the names of the teams: winning, drawing, conceding, conceding and goal difference.

1 Xiamen Blue Lion1310212681832

2 Changchun Yatai13841361224 28

3 Guangzhou Sunshine Spring 13 7 4 2 22 6 16 25

4 Jiangsu Shuntian136612010/0 24

5 Babei Greentown, Zhejiang 13 7 2 4 20 12 8 23

6 Qingdao Hisense136431614222

7 Henan Jianye13 4541415-17

8 Yanbian135172219316

9 Shanghai Jiucheng13 364 2118 315

10 Nanjing You133642018215.

1 1 Chengdu Wuniu13418 2030-1013

12 Hunan Xiang Army133281025-1511

13 Dalian longwa13319930-2110

14 Harbin national strength 13 0 13 0 39-39 0

3. Party A and Party B are trainee salesmen of a company, selling "Little Swan" washing machine.

Their sales from June 5 to August are shown in the following table:

Sales volume in a month

Sales volume of Party B (unit: Taiwan)

(Unit: Taiwan Province)

1July 5

February 8-6

March 6-5

April 7-6

May 6-7

June 6-7

July 7-8

7 and 9 August

(1) Draw a line chart of the monthly sales of Party A and Party B in the coordinate system given above: (Party A uses a solid line; B is indicated by dashed lines)

(2) Please write two pieces of information about the sales of Party A and Party B in these eight months according to the line chart in (1).

② .

4. (The full mark of this question is 10) In order to understand the development of the activity of "honoring parents and starting from housework" in schools. The school selected 50 senior two students to investigate for one week (calculated by seven days).

Service time (unit: hours), get a set of data and draw the following table. please

Packet frequency cumulative percentage

0.55 ~ 1.05 plus 14 0.28

Zheng Zheng 1.05 ~ 1.55

1.55 ~ 2.05 plus 7

2.05~2.55 4 0.08

2.55 ~ 3.05 plus 5 0. 10

3.05~3.55 3

3.55~4.05 0.04

Total 50 50 1.00

Answer the following questions according to the table:

(1) Complete the frequency distribution table.

(2) From the above information, the time spent doing housework every week.

Percentage of students who do not exceed 1.5 hours.

(3) Making statistical charts reflecting the survey results.

(4) In view of the above situation, write a sentence that advocates "respecting parents and loving labor" within 20 words.

Fourth, answer questions:

1. As shown in the figure, in the quadrilateral ABCD, point E is on the edge CD, and AE and BE are connected. The following five relations are given: ① ad ‖ BC; ②DE = CE； ③∠ 1=∠2; ④∠3=∠4; ⑤ AD+BC = AB。 Take three of them as problems and the other two as conclusions to form a proposition.

(1) Write a true proposition with serial number (writing form: if ×××,

Then xx), and give proof:

(2) Write three true propositions with serial numbers (without proof);

(3) Extra points: there are more than four true propositions. If you think about it, you can have more.

Write a few real questions, and each additional real question will be given to you 1 point.

Add 2 points at most.